1. Field of the Invention
The present invention relates generally to a mathematical teaching or learning method in which numerical quantities can be represented directly on the number. By this means, many of the basic functions of mathematics such as learning ones, tens, hundreds, thousands columns, addition, multiplication, exponents, subtraction, division, fractions (addition, subtraction, multiplication, division of fractions), negative numbers (addition, subtraction, multiplication, division of negative numbers both fractional and whole), decimals, and the like are quantitatively represented, viewed, manipulated, and solved directly on the numbers themselves. The invention represents a method. The numbers may be represented on a mutable substrate, such as paper and a kit for practicing the method is part of the invention. The method of the invention may be adapted to other platforms such as computer programs and video games within the scope of this invention.
2. Description of the Prior Art
There is a diverse and eclectic body of prior art directed to mathematical learning and teaching. During a search directed to the subject matter of this invention, the following US patents were noted.
U.S. Design Pat. No. 163,085 (Bishop) and Utility Pat. Nos. 367,223 (Moody), U.S. Pat. No. 2,842,870 (Lilly), U.S. Pat. No. 3,357,116 (Bazacos), U.S. Pat. No. 4,808,111 (Pratt) and U.S. Pat. No. 5,040,987 (Frazier).
The Lilly patent discloses manipulatives for representing various numbers and numerical representations of numbers. Referring to FIGS. 5 and 6, there are illustrated ten disks (50) representing a one in the tens column. The disks, however, are received in a receptacle in which they can not be further manipulated.
The Bazacos patent discloses a device comprising a display board, supports for hanging numbers, i.e. one through nine, on the board and pegs or other indicia attached to the board, adjacent each support, and representing the number which is to be hung on each support.
The Pratt patent discloses a device comprising a number rack with variously shaped openings, number plates, with corresponding shapes, which can be inserted only in the appropriate recess, and indicia adjacent each opening corresponding in number to the number that is to be received in the recess. This appears to be an "improvement" on the device disclosed in the Bazacos patent.
The Moody patent discloses number cards including dots.
The other patents appear to have only marginal relevance to the present invention.
A series of workbooks published in 1991, entitled NO MEMORIZATION ADDITION AND SUBTRACTION, disclose several techniques for adding and subtracting numbers. One of the workbooks, entitled SUBTRACTION WORKBOOK 2, discloses printed digits, i.e., whole numbers from one to nine, with a corresponding number of dots on the printed digit. This workbook also discloses the use of toothpicks to represent the value of a digit in the one's place and of ten bundled toothpicks to represent the value of a digit in the ten's place.
There are many math resources that are available to assist teachers in teaching students. Math manipulatives are generally known and can comprise tiles, blocks, measuring devices and the like which give students hands-on learning opportunities. Some currently available math resources are discussed in a catalog called "Summit Learning" for Spring, 1996.
Despite the abundance of mathematics teaching and learning materials and methods, there remains a need for a simple, effective and versatile method for teaching and learning basic and advanced math skills.